Driveline Dynamics

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Driveline Dynamics

• Engine Dynamics
• Driveline and Efficiency
• Gearbox and Clutch Dynamics
• Gearbox Design

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Driveline Components
Driveline components of a rear wheel drive
vehicle.
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Engine Dynamics

• The maximum attainable power Pe of an internal
  combustion
• engine is a function of the engine angular
  velocity ?e.
• This function must be determined experimentally,
• However, the function Pe Pe (?e), which is
  called the
• power performance function, can be estimated by
  a third-order polynomial

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Power-Toque Performance
A sample of power and torque performances for a
spark ignition engine
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Power performance curves for the Porsche 911 and
Corvette Z06
An example of power performance in a spark
ignition engine with constant efficiency contours
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Performance curves of an ideal engine having a
linear torque-speed relationship Te 0.14539 ?e.
Power and torque performance curves for an ideal
engine.
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Driveline and Efficiency
Driveline components of a rear wheel drive
vehicle.
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The input and output torque and angular velocity
of each driveline component
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Gear Box and Clutch Dynamics
A sample of a gear-speed plot for a gearbox
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Wheel torque-speed Equation at each gear ni of a
gearbox, and the envelope curve simulating an
ideal engine behavior
An example for the acceleration capacity ax as a
fucntion of forward speed vx.
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Gear Box Design (Transmision Ratios)

• 1. We may design the differential transmission
  ratio nd and the final gear nn such that the
  final gear nn is a direct gear, nn 1, when the
  vehicle is moving at the moderate highway speed.
  Using nn 1 implies that the input and output of
  the gearbox are directly connected with each
  other. Direct engagement maximizes the mechanical
  efficiency of the gearbox.
• 2. We may design the differential transmission
  ratio nd and the final gear nn such that the
  final gear nn is a direct gear, nn 1, when the
  vehicle is moving at the maximum attainable
  speed.
• 3. The first gear n1 may be designed by the
  maximum desired torque at driving wheels. Maximum
  torque is determined by the slope of a desired
  climbing road.

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Gear Box Design (Transmision Ratios)
4. We can find the intermediate gears using the
gear stability condition. Stability condition
provides that the engine speed must not exceed
the maximum permissible speed if we gear down
from ni to ni -1, when the engine is working at
the maximum torque in ni
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Geometric Gear Box Design
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Geometric Ratio Gearbox Design
A gear-speed plot for a progressive gearbox
design.
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Example 140 A gearbox with three gears.
The power performance curve (4.121) and its
working range.
The gear-speed plot for a three-gear gearbox.
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Better performance with a four-gear gearbox. (141)
The gear-speed plot for Example 141.
The power performance curve (4.170) and its
working range.
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Summary Power

• The maximum attainable power Pe of an internal
  combustion engine is a function of the engine
  angular velocity ?e.
• ?M is the angular velocity, measured in rad/
  s, at which the engine power reaches the maximum
  value PM, measured in W Nm/ s.

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Torque
The engine torque Te is the torque that provides
Pe
We use a gearbox to make the engine approximately
work at a constant power close to the PM . To
design a gearbox we use two equations the
speed equation
An ideal engine is the one that produces a
constant power regardless of speed. For the ideal
engine, we have
Traction Equation
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Conclusions

• These equations state that the forward velocity
  vx of a vehicle is proportional to the angular
  velocity of the engine ?e,
• The tire traction force Fx is proportional to
  the engine torque Te, where, Rw is the effective
  tire radius.
• nd is the differential transmission ratio, ni is
  the gearbox transmission ratio in gear number i,
  and ? is the overall driveline efficiency